Hindus And Mathematics

[Guest guest]

'In science, more than in any other human institution, it is necessary

to search out the past in order to understand the present and to control

the future.'

 

-- J D Bernal, Science in History

 

As we hurtle into a new millennium, we would do well to reflect where

all those 0s came from. The greatness that was Greece and the grandeur

that was Rome started their numeral systems at one. The Arabs brought

the modern numerals, including zero, to Europe centuries ago. But while

1, 2, 3, are commonly and mistakenly referred to as the " Arabic "

numerals, they actually originated in India, and are but one of many

achievements that became treasures lost to the oblivion of history.

 

India is the epitome of diversity in all respects, geographically

and culturally. From such diversity has bloomed the myriad blossoms of

science and mathematics. Indian science flowered long before the

classical age of Europe and flourishes to this day. .

 

India must be credited with the primacy of the invention of

unaccountably finite principles and theorems that have been granted to

later Arabs and Europeans. In celebrating India's contribution to

learning we shall find a deep and long-nurtured reverent and respectful

love of learning.

 

There is still much to be learned from ancient Indian science. The

depths of the Vedas and other scriptures, as well as more " scholarly "

extant work, offer much to the modern world of science. Indeed, we can

all profit from an in-depth examination of ancient Indian science. Yet

it is a sad testament to our community's inability to transmit our

heritage to our youth that most of our youngsters don't know the

difference between Brahmagupta and Brahmaputra.

 

This article focuses on some of the more important and relevant

inventions and discoveries of ancient Indians and attempts to analyze

the reasons why these scientists never received their due credit.

 

In the 16th century, there grew a tendency in Europe to trace

scientific thought to the achievements of Mediterranean antiquity. This

direct link between modern science and ancient Greece is increasingly

perpetuated by a flourishing literature in the cause of a simplistic,

but false, understanding of the history of science. Most Western

historians preach the tale that a Greek miracle led to the dawn of

science. The facts of older civilizations are cursorily covered and

mainly for the perverted purpose of showing why there was no real

science before the Greeks.

 

Arnold Reymand echoed these sentiments well: " Compared to

empirical and fragmentary knowledge which the peoples of the East had

laboriously gathered together during long centuries, Greek science

constitutes a veritable miracle. "

 

 

However, historian Will Durant correctly observed: " Europe and

America are the spoiled child and grandchild of Asia and have never

quite realized the wealth of their pre-classical inheritance. " Most

Western study of ancient India has been a tunnel vision dominated by a

prefabricated psychology. The parochial provincialism of mindless

Eurocentrism has distorted the history of civilization as originating in

Greece while summing up India's contribution in a line or two.

 

However, our own apathy in addition to Western neglect has led to

the demise of ancient Indian science from the pages of history. The

disguised racism of some historians notwithstanding, we must share the

blame for this tragedy. It is imperative that we shed our ignorance and

elucidate what for countless centuries has been buried in the recess of

history.

 

India's most important contribution to science is nothing: the

concept of nothing, or zero, is central to the understanding of all

else. It is time that we raise out scientific heritage from what it is

today: nothing.

 

No ancient civilization possessed more talent or accomplished more

feats in mathematics than India. For instance, the most ingenious

creation in all of mathematics, the decimal system, of which the famed

mathematician LaPlace wrote: " It is India that gave us the ingenious

method of expressing all numbers by 10 symbols, a profound and important

idea which appears so simple to us now that we ignore its true merit.

But its very simplicity, the great ease which it has lent to all

computations, puts our arithmetic in the first rank of useful

inventions; and we shall appreciate the grandeur of this achievement the

more when we remember that it escaped the genius of Archimedes and

Apollonius, two of the greatest men produced by antiquity. "

 

These misnomered " Arabic " numerals appeared on the Rock Edicts of

Ashoka (256 BC), a thousand years before they appeared in the Arabic

literature. Even those few who know this fact know ittle more about the

myriad contributions of Indian mathematics.

 

India's work in science is young as a secular pursuit

but old as an auxiliary interest of her priests. Science started with

the priests, originated in astronomy and mathematics governing religious

festivals, and was preserved in the temples and transmitted through the

generations.

 

Consider the most famous elementary theorem in mathematics: the

so-called Pythagorean theorem, which states that the square of the

hypotenuse of a right triangle equals the sum of the squares of the

other two sides. The Sulvasutras (collection of rules concerning

measurements) of Baudhayana (600 BC) describe this identity almost 200

years before Pythagoras: " The diagonal of an oblong produces by itself

both the areas which the two sides of the oblong produce separately. "

 

Aryabhata (476-520 AD), the father of Indian mathematics and

astronomy, computed pi to 3.1416, a value not equaled in Europe until

Purbach (1423-61). Pi is computed to 11 digits in the Karanapaddhati

work (15th century) as 3.1415926535, a value not equaled in Europe until

much later. More importantly, Indian mathematicians knew algebra at

least as early as the 5th century AD Known as Bijaganitam, algebra (a

corruption of the Arabic word Al-Jabr) was used extensively in

astronomical calculations and referred to by Aryabhata in his treatise

Aryabhattiya. This science was couriered to the West by the Arabs.

 

Trigonometry too was known to Indian mathematicians and astronomers

before their European counterparts. It was used in India from the Gupta

period (3rd century AD) onwards, and the Surya- Siddhanta (4th century

AD) gives a table of sines.

 

Indian atomic theory greatly predates Democritus (430 BC). Kashyapa

(aka Kanada), in his Vaisheshika Sutra, formulated an advanced theory of

atomic structure in the 6th century BC. He also stated the principle of

volume displacement long before Archimedes. Pakudha Kayayana (580 BC), a

contemporary of Buddha, taught atomic theory by propounding the theory

that undifferentiated potential matter (tanmatra) forms the universal

energy of the cosmos by forming atoms.

 

Brahmagupta (598-660 AD) anticipated the gravitational theory:

" Things fall to the ground not because of any inherent force within but

because of the pull from the earth. " A century before Brahmagupta,

Varahamihira claimed that objects remain on the earth's surface due to

an internal attractive force and that a similar force keeps celestial

bodies in their positions. In fact, the ancient Sanskrit has a word for

gravity -- Gurutvakarshan.

 

Aryabhata also proposed the heliocentric theory a millennium before

Copernicus, who is generally credited with this revolutionary idea. In

poetic form, Aryabhata stated that the earth's diurnal rotation on its

axis produced the daily rising and setting of planets and stars. In

fact, the Sandhya Vandanam (morning prayers to the sun), dating back to

the Vedic age, contains numerous references to the sun as the center of

the solar system.

 

Long before Columbus staked his claim that the world was round,

Aryabhata recognized that the earth was spherical and Brahmagupta gave a

figure of 36,000 km for the earth's circumference, not far from the

actual value.

 

And a word about the game that is so popular among us

Indians -- chess. It is so old that half the world claims it.

Archaeologists generally believe it arose in India, where the oldest

indisputable

appearance in 750 AD. The word chaturanga became transformed into the Arabic

shatranj and finally chess.

 

We hope the foregoing non-exhaustive recital will serve to kindle

pride and interest in our collective heritage. Trying to forge links

with the past without teaching about our contributions is akin to

planting cut flowers. Parents must pass on knowledge about our past to

our youth, much like a relay race, lest our leaders of tomorrow grow

bereft of vital knowledge and become rudderless in an information-driven

world.

 

BY THE AMBATI FAMILY.

(The Ambati family has conducted the Educational

Excellence Program, for middle and high school students, for the

last decade. These free classes are held every Saturday at the

Swaminarayan Temple in Flushing, New York.